Isomorphism identification algorithm and database generation for planar 2-6 DOFs fractionated kinematic chains combined by two or three non-fractionated kinematic chains

Abstract Existing methods for synthesizing fractionated kinematic chains usually avoid generating isomorphic fractionated kinematic chains rather than identifying isomorphic chains. Consequently, no isomorphism identification algorithm for fractionated kinematic chains, especially those with complex structures, has been reported. This study, based on a new isomorphism identification algorithm, proposes a systematic method to synthesize all possible non-isomorphic fractionated kinematic chains with up to 16 links and up to 6 degrees of freedom (DOFs), which are combined by two or three non-fractionated kinematic chains. First, the structural constraint equations are presented to obtain all possible combinations of fractionated kinematic chains. Second, the two concepts of a split-vertex characteristic graph and a combined characteristic graph are developed to acquire the corresponding combined characteristic code, which is the unique representation of planar fractionated kinematic chains and is applied to identify the isomorphism problem. Then, all possible 2-6 DOFs non-isomorphic fractionated kinematic chains combined by two or three non-fractionated kinematic chains are synthesized. Moreover, the corresponding databases of the synthesized fractionated kinematic chains are established. Finally, the synthesis methods and results of this study and the ones in the existing literature are compared and discussed in detail.